Package 'greed'

Description

An S4 class to represent an abstract optimization algorithm.

Description

Display the list of every currently available optimization algorithm

Usage

available_algorithms()

Description

Display the list of every currently available DLVM

Usage

available_models()

Description

A network of books about US politics published around the time of the 2004 presidential election and sold by the online bookseller Amazon.com. Edges between books represent frequent co-purchasing of books by the same buyers. The network was compiled by V. Krebs and is unpublished, but can found on Krebs' web site. Thanks to Valdis Krebs for permission to post these data on this web site.

Usage

data(Books)

Format

An object of class list with two fields;

X

network adjacency matrix as a sparseMatrix of size 105x105

label

a factor of length (size 105) with levels "l", "n", or "c" to indicate whether the books are liberal, neutral, or conservative

Examples

data(Books)

Method to extract the clustering results from an IclFit-class object

Description

This method take a IclFit-class object and return an integer vector with the cluster assignments that were found.

Usage

clustering(fit)

## S4 method for signature 'IclFit'
clustering(fit)

Arguments

Value

an integer vector with cluster assignments. Zero indicates noise points.

Methods (by class)

• IclFit: IclFit-class method

Extract parameters from an DcLbmFit-class object

Description

Extract parameters from an DcLbmFit-class object

Usage

## S4 method for signature 'DcLbmFit'
coef(object)

Arguments

Value

a list with the model parameters estimates (MAP), the fields are:

• 'pirows': row cluster proportions

• 'picols': row cluster proportions

• 'thetakl': between clusters connection probabilities (matrix of size Krow x Kcol),

• 'gammarows': rows degree correction parameters (size Nrows),

• 'gammacols': cols degree correction parameters (size Ncols),

Extract parameters from an DcSbmFit-class object

Description

Extract parameters from an DcSbmFit-class object

Usage

## S4 method for signature 'DcSbmFit'
coef(object)

Arguments

Details

in case of undirected graph

Value

a list with the model parameters estimates (MAP), the fields are the following for "directed" models :

• 'pi': cluster proportions

• 'thetakl': between cluster normalized connection intensities (matrix of size K x K),

• gammain: node in-degree correction parameter

• gammaout: node out-degree correction parameter

And as follow for un-directed models : #'

• 'pi': cluster proportions

• 'thetakl': between cluster normalized connection intensities (matrix of size K x K),

• gamma: node degree correction parameter

Extract mixture parameters from DiagGmmFit-class object

Description

Extract mixture parameters from DiagGmmFit-class object

Usage

## S4 method for signature 'DiagGmmFit'
coef(object)

Arguments

Value

a list with the mixture parameters estimates (MAP), the fields are:

• 'pi': cluster proportions

• 'muk': cluster means

• 'Sigmak': cluster co-variance matrices

Extract mixture parameters from GmmFit-class object

Description

Extract mixture parameters from GmmFit-class object

Usage

## S4 method for signature 'GmmFit'
coef(object)

Arguments

Value

a list with the mixture parameters estimates (MAP), the fields are:

• 'pi': cluster proportions

• 'muk': cluster means

• 'Sigmak': cluster co-variance matrices

Extract parameters from an IclFit-class object

Description

Extract parameters from an IclFit-class object

Usage

## S4 method for signature 'IclFit'
coef(object)

Arguments

Details

The results depends of the used model, in case the method is not yet implemented for a model, this generic method will be used. Which will return the obs_stats slot of the model.

Value

a list with the model parameters estimates (MAP)

Extract parameters from an LcaFit-class object

Description

Extract parameters from an LcaFit-class object

Usage

## S4 method for signature 'LcaFit'
coef(object)

Arguments

Value

a list with the model parameters estimates (MAP), the fields are:

• 'pi': cluster proportions

• 'thetav': cluster profile probabilities (list of matrix of size K x Dv),

Extract parameters from an MoMFit-class object

Description

Extract parameters from an MoMFit-class object

Usage

## S4 method for signature 'MoMFit'
coef(object)

Arguments

Value

a list with the model parameters estimates (MAP), the fields are:

• 'pi': cluster proportions

• 'thetak': cluster profile probabilities (matrix of size K x D),

Extract mixture parameters from MoRFit-class object using MAP estimation

Description

Extract mixture parameters from MoRFit-class object using MAP estimation

Usage

## S4 method for signature 'MoRFit'
coef(object)

Arguments

Value

a list with the mixture parameters estimates (MAP), the fields are:

• 'pi': cluster proportions

• 'A': cluster regression matrix

• 'Sigmak': cluster noise co-variance matrices

Extract parameters from an MultSbmFit-class object

Description

Extract parameters from an MultSbmFit-class object

Usage

## S4 method for signature 'MultSbmFit'
coef(object)

Arguments

Value

a list with the model parameters estimates (MAP), the fields are:

• 'pi': cluster proportions

• 'thetakl': cluster profile probabilities (array of size K x K x D),

Extract parameters from an SbmFit-class object

Description

Extract parameters from an SbmFit-class object

Usage

## S4 method for signature 'SbmFit'
coef(object)

Arguments

Value

a list with the model parameters estimates (MAP), the fields are:

• 'pi': cluster proportions

• 'thetakl': between clusters connections probabilities (matrix of size K x K)

Description

An S4 class to represent a combined clustering models, where several models are used to model different datasets. A conditional independence assumption between the view knowing the cluster is made.

Usage

CombinedModels(models, alpha = 1)

Arguments

Details

The filed name in the models list must match the name of the list use to provide the datasets to cluster together.

Value

a CombinedModels-class object

See Also

CombinedModelsFit-class, CombinedModelsPath-class

Other DlvmModels: DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MoR, MultSbm, Sbm, greed()

Examples

CombinedModels(models = list(continuous = GmmPrior(), discrete = LcaPrior()))

Description

An S4 class to represent a fit of a degree corrected stochastic block model for co_clustering, extend IclFit-class.

Slots

model

a DcSbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

extractSubModel,CombinedModelsPath,character-method

Description

An S4 class to represent a hierarchical fit of a degree corrected stochastic block model, extend IclPath-class.

Slots

model

a DcSbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

path

a list of size K-1 with each part of the path described by:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• cl: vector of cluster indexes

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats: a list with the elements:

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

extractSubModel,CombinedModelsPath,character-method

Description

This method take a DcLbmPath-class and an integer K and return the solution from the path with K clusters

Usage

## S4 method for signature 'DcLbmPath'
cut(x, K)

Arguments

Value

an IclPath-class object with the desired number of cluster

Description

This method take a IclPath-class object and an integer K and return the solution from the path with K clusters

Usage

## S4 method for signature 'IclPath'
cut(x, K)

Arguments

Value

an IclPath-class object with the desired number of cluster

Description

An S4 class to represent a degree corrected stochastic block model for co_clustering of bipartite graph. Such model can be used to cluster graph vertex, and model a bipartite graph adjacency matrix $X$ with the following generative model :

$\pi \sim Dirichlet(\alpha)$

$Z_i^r \sim \mathcal{M}(1,\pi^r)$

$Z_j^c \sim \mathcal{M}(1,\pi^c)$

$\theta_{kl} \sim Exponential(p)$

$\gamma_i^r\sim \mathcal{U}(S_k)$

$\gamma_i^c\sim \mathcal{U}(S_l)$

$X_{ij}|Z_{ik}^cZ_{jl}^r=1 \sim \mathcal{P}(\gamma_i^r\theta_{kl}\gamma_j^c)$

The individuals parameters $\gamma_i^r,\gamma_j^c$ allow to take into account the node degree heterogeneity. These parameters have uniform priors over simplex $S_k$. These classes mainly store the prior parameters value $\alpha,p$ of this generative model. The DcLbm-class must be used when fitting a simple Diagonal Gaussian Mixture Model whereas the DcLbmPrior-class must be sued when fitting a CombinedModels-class.

Usage

DcLbmPrior(p = NaN)

DcLbm(alpha = 1, p = NaN)

Arguments

Value

a DcLbmPrior-class

a DcLbm-class object

See Also

DcLbmFit-class, DcLbmPath-class

Other DlvmModels: CombinedModels, DcSbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MoR, MultSbm, Sbm, greed()

Examples

DcLbmPrior()
DcLbmPrior(p = 0.7)
DcLbm()
DcLbm(p = 0.7)

Description

An S4 class to represent a fit of a degree corrected stochastic block model for co_clustering, extend IclFit-class.

Slots

model

a DcLbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

Krow

number of extracted row clusters

Kcol

number of extracted column clusters

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• din: numeric vector of size K which store the sums of in-degrees for each clusters

• dout: numeric vector of size K which store the sums of out-degrees for each clusters

• x_counts: matrix of size K*K with the number of links between each pair of clusters

• co_x_counts: matrix of size Krow*Kcol with the number of links between each pair of row and column cluster

clrow

a numeric vector with row cluster indexes

clcol

a numeric vector with column cluster indexes

Nrow

number of rows

Ncol

number of columns

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

coef,DcLbmFit-method

Description

An S4 class to represent a fit of a degree corrected stochastic block model for co_clustering, extend IclPath-class.

Slots

model

a DcLbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

Krow

number of extracted row clusters

Kcol

number of extracted column clusters

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• din: numeric vector of size K which store the sums of in-degrees for each clusters

• dout: numeric vector of size K which store the sums of out-degrees for each clusters

• x_counts: matrix of size K*K with the number of links between each pair of clusters

• co_x_counts: matrix of size Krow*Kcol with the number of links between each pair of row and column cluster

clrow

a numeric vector with row cluster indexes

clcol

a numeric vector with column cluster indexes

Nrow

number of rows

Ncol

number of columns

path

a list of size K-1 with each part of the path described by:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• cl: vector of cluster indexes

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats: a list with the elements:

  • counts: numeric vector of size K with number of elements in each clusters

  • din: numeric vector of size K which store the sums of in-degrees for each clusters

  • dout: numeric vector of size K which store the sums of out-degrees for each clusters

  • x_counts: matrix of size K*K with the number of links between each pair of clusters

  • co_x_counts: matrix of size Krow*Kcol with the number of links between each pair of row and column cluster

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

ggtreerow

data.frame with complete merge tree of row clusters for easy plotting with ggplot2

ggtreecol

data.frame with complete merge tree of column clusters for easy plotting with ggplot2

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

plot,DcLbmPath,missing-method

Description

An S4 class to represent a Degree Corrected Stochastic Block Model. Such model can be used to cluster graph vertex, and model a square adjacency matrix $X$ with the following generative model :

$\pi \sim Dirichlet(\alpha)$

$Z_i \sim \mathcal{M}(1,\pi)$

$\theta_{kl} \sim Exponential(p)$

$\gamma_i^+,\gamma_i^- \sim \mathcal{U}(S_k)$

$X_{ij}|Z_{ik}Z_{jl}=1 \sim \mathcal{P}(\gamma_i^+\theta_{kl}\gamma_j^-)$

The individuals parameters $\gamma_i^+,\gamma_i^-$ allow to take into account the node degree heterogeneity. These parameters have uniform priors over the simplex $S_k$ ie. $\sum_{i:z_{ik}=1}\gamma_i^+=1$. These classes mainly store the prior parameters value $\alpha,p$ of this generative model. The DcSbm-class must be used when fitting a simple Degree Corrected Stochastic Block Model whereas the DcSbmPrior-class must be used when fitting a CombinedModels-class.

Usage

DcSbmPrior(p = NaN, type = "guess")

DcSbm(alpha = 1, p = NaN, type = "guess")

Arguments

Value

a DcSbmPrior-class object

a DcSbm-class object

See Also

DcSbmFit-class, DcSbmPath-class

Other DlvmModels: CombinedModels, DcLbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MoR, MultSbm, Sbm, greed()

Examples

DcSbmPrior()
DcSbmPrior(type = "undirected")
DcSbm()
DcSbm(type = "undirected")

Description

An S4 class to represent a fit of a degree corrected stochastic block model for co_clustering, extend IclFit-class.

Slots

model

a DcSbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• din: numeric vector of size K which store the sums of in-degrees for each clusters

• dout: numeric vector of size K which store the sums of out-degrees for each clusters

• x_counts: matrix of size K*K with the number of links between each pair of clusters

obs_stats_cst

a list with the following elements:

• din_node: node in-degree, a vector of size N

• dout_node: node in-degree vector of size N

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

coef,DcSbmFit-method

Description

An S4 class to represent a hierarchical fit of a degree corrected stochastic block model, extend IclPath-class.

Slots

model

a DcSbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• din: numeric vector of size K which store the sums of in-degrees for each clusters

• dout: numeric vector of size K which store the sums of out-degrees for each clusters

• x_counts: matrix of size K*K with the number of links between each pair of clusters

path

a list of size K-1 with each part of the path described by:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• cl: vector of cluster indexes

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats: a list with the elements:

  • counts: numeric vector of size K with number of elements in each clusters

  • din: numeric vector of size K which store the sums of in-degrees for each clusters

  • dout: numeric vector of size K which store the sums of out-degrees for each clusters

  • x_counts: matrix of size K*K with the number of links between each pair of clusters

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

plot,DcSbmFit,missing-method

Description

An S4 class to represent a multivariate diagonal Gaussian mixture model. The model corresponds to the following generative model:

$\pi \sim Dirichlet(\alpha)$

$Z_i \sim \mathcal{M}(1,\pi)$

$\lambda_k^{(d)} \sim \mathcal{G}(\kappa,\beta)$

$\mu_k^{(d)} \sim \mathcal{N}(\mu,(\tau \lambda_k)^{-1})$

$X_{i.}|Z_{ik}=1 \sim \mathcal{N}(\mu_k,\lambda_{k}^{-1})$

with $\mathcal{G}(\kappa,\beta)$ the Gamma distribution with shape parameter $\kappa$ and rate parameter $\beta$. These classes mainly store the prior parameters value ($\alpha,\tau,\kappa\beta,\mu$) of this generative model. The DiagGmm-class must be used when fitting a simple Diagonal Gaussian Mixture Model whereas the DiagGmmPrior-class must be sued when fitting a CombinedModels-class.

Usage

DiagGmmPrior(tau = 0.01, kappa = 1, beta = NaN, mu = NaN)

DiagGmm(alpha = 1, tau = 0.01, kappa = 1, beta = NaN, mu = NaN)

Arguments

Value

a DiagGmmPrior-class object

a DiagGmm-class object

References

Bertoletti, Marco & Friel, Nial & Rastelli, Riccardo. (2014). Choosing the number of clusters in a finite mixture model using an exact Integrated Completed Likelihood criterion. METRON. 73. 10.1007/s40300-015-0064-5. #'

See Also

DiagGmmFit-class, DiagGmmPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DlvmPrior-class, Gmm, Lca, MoM, MoR, MultSbm, Sbm, greed()

Examples

DiagGmmPrior()
DiagGmmPrior(tau = 0.1)
DiagGmm()
DiagGmm(tau = 0.1)

Description

An S4 class to represent a fit of a multivariate diagonal Gaussian mixture model, extend IclFit-class.

Slots

model

a DiagGmm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• regs: list of size $K$ with statistics for each clusters

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

coef,DiagGmmFit-method

Description

An S4 class to represent a hierarchical fit of a diagonal gaussian mixture model, extend IclPath-class.

Slots

model

a DiagGmm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• regs: list of size $K$ with statistics for each clusters

path

a list of size K-1 with each part of the path described by:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• cl: vector of cluster indexes

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats: a list with the following elements:

  • counts: numeric vector of size K with number of elements in each clusters

  • regs: list of size $K$ with statistics for each clusters

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

plot,DiagGmmFit,missing-method

Description

An S4 class to represent an abstract generative model

Slots

alpha

a numeric vector of length 1 which define the parameters of the Dirichlet over the cluster proportions (default to 1)

Description

An S4 class to represent an abstract generative model

Slots

alpha

a numeric vector of length 1 which define the parameters of the Dirichlet over the cluster proportions (default to 1)

See Also

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, Gmm, Lca, MoM, MoR, MultSbm, Sbm, greed()

Extract a part of a CombinedModelsPath-class object

Description

Extract a part of a CombinedModelsPath-class object

Usage

extractSubModel(sol, sub_model_name)

## S4 method for signature 'CombinedModelsPath,character'
extractSubModel(sol, sub_model_name)

Arguments

Value

a IclFit-class object of the relevant class

Methods (by class)

• sol = CombinedModelsPath,sub_model_name = character: CombinedModelsPath method

Description

Zalando fashionmnist dataset, sample of 1 000 Zalando's article images from the test set.

Usage

data(fashion)

Format

An object of class matrix with a random sample of 1000 images (one per rows) extracted from the fashionmnist dataset.

Source

https://github.com/zalandoresearch/fashion-mnist

References

Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms. Han Xiao, Kashif Rasul, Roland Vollgraf (2017) (arXiv:1708.07747).

Examples

data(fashion)

Description

A random sample of 6000 players from the FIFA videogame with various statistics on all player ranging from position, cost in the game, capacity in offense/defense, speed, etc. Two columns pos_x, pos_y with average player possible positions (in opta coordiantes) were derived from the raw data. was also u.

Usage

data(Fifa)

Format

An R data.frame with columns containing each of the descriptive statistics of a player.

Source

https://www.kaggle.com/stefanoleone992/fifa-20-complete-player-dataset?select=players_20.csv

Examples

data(Fifa)

Description

Network of American football games between Division IA colleges during regular season Fall 2000.

Usage

data(Football)

Format

An object of class list with two fields;

X

network adjacency matrix as a sparseMatrix of size 115x115

label

vector of teams conferences of size 115 with the following encoding (0 = Atlantic Coast, 1 = Big East, 2 = Big Ten, 3 = Big Twelve, 4 = Conference USA, 5 = Independents, 6 = Mid-American, 7 = Mountain West, 8 = Pacific Ten, 9 = Southeastern, 10 = Sun Belt, 11 = Western Athletic)

References

M. Girvan and M. E. J. Newman, Community structure in social and biological networks, Proc. Natl. Acad. Sci. USA 99, 7821-7826 (2002)

Examples

data(Football)

Description

An S4 class to represent a genetic algorithm (extends Alg-class class).

Usage

Genetic(pop_size = 100, nb_max_gen = 20, prob_mutation = 0.25, sel_frac = 0.75)

Arguments

Value

a Genetic-class object

Functions

• Genetic: Genetic algorithm class constructor

Slots

pop_size

size of the solutions populations (default to 10)

nb_max_gen

maximal number of generation to produce (default to 4)

prob_mutation

probability of mutation (default to 0.25)

sel_frac

fraction of best solutions selected for crossing (default to 0.75)

Examples

Genetic()
Genetic(pop_size = 500)

Description

An S4 class to represent a multivariate Gaussian mixture model. The model corresponds to the following generative model:

$\pi \sim Dirichlet(\alpha)$

$Z_i \sim \mathcal{M}(1,\pi)$

$V_k \sim \mathcal{W}(\varepsilon^{-1},n_0)$

$\mu_k \sim \mathcal{N}(\mu,(\tau V_k)^{-1})$

$X_{i}|Z_{ik}=1 \sim \mathcal{N}(\mu_k,V_{k}^{-1})$

with $\mathcal{W}(\varepsilon^{-1},n_0)$ the Wishart distribution. The Gmm-class must be used when fitting a simple Gaussian Mixture Model whereas the GmmPrior-class must be used when fitting a CombinedModels-class.

Usage

GmmPrior(tau = 0.01, N0 = NaN, mu = NaN, epsilon = NaN)

Gmm(tau = 0.01, N0 = NaN, mu = NaN, epsilon = NaN, alpha = 1)

Arguments

Value

a GmmPrior-class object

a Gmm-class object

References

Bertoletti, Marco & Friel, Nial & Rastelli, Riccardo. (2014). Choosing the number of clusters in a finite mixture model using an exact Integrated Completed Likelihood criterion. METRON. 73. 10.1007/s40300-015-0064-5.

See Also

GmmFit-class, GmmPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Lca, MoM, MoR, MultSbm, Sbm, greed()

Examples

GmmPrior()
GmmPrior(tau = 0.1)
Gmm()
Gmm(tau = 0.1, alpha = 0.5)

Description

An S4 class to represent a fit of a multivariate mixture of regression model, extend IclFit-class.

Slots

model

a GmmPrior-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• regs: list of size $K$ with statistics for each clusters

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

coef,GmmFit-method

Description

Make a matrix of plots with a given data and gmm fitted parameters with ellipses.

Usage

gmmpairs(sol, X)

Arguments

Value

a ggplot2 graphic

Description

An S4 class to represent a hierarchical fit of a gaussian mixture model, extend IclPath-class.

Slots

model

a GmmPrior-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• gmm: list of size $K$ with statistics for each clusters

path

a list of size K-1 with each part of the path described by:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats: a list with the following elements:

  • counts: numeric vector of size K with number of elements in each clusters

  • gmm: list of size $K$ with statistics for each clusters

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

plot,GmmFit,missing-method

Description

This function is the main function for fitting Dlvms with greed. In the simplest case you may only provide a dataset and greed will find a suitable one. The accepted classes for X depends on the generative used which can be specified with the model argument. See the DlvmPrior-class and the derived classes for details.

Greed enables the clustering of networks and count data matrix with different models. Model selection and clustering are performed in combination by optimizing the Integrated Classification Likelihood. Optimization is performed thanks to a combination of greedy local search and a genetic algorithm. The main entry point is the greed function to perform the clustering, which is documented below. The package also provides sampling functions for all the implemented DLVMs.

Usage

greed(X, model = find_model(X), K = 20, alg = Hybrid(), verbose = FALSE)

Arguments

Value

an IclPath-class object

See Also

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MoR, MultSbm, Sbm

Examples

sbm <- rsbm(50, c(0.5, 0.5), diag(2) * 0.1 + 0.01)
sol <- greed(sbm$x, model = Sbm())
table(sbm$cl,clustering(sol))

Description

Compute the entropy of a discrete sample

Usage

H(cl)

Arguments

Value

the entropy of the sample

Examples

cl <- sample(2, 500, replace = TRUE)
H(cl)

Description

An S4 class to represent an hybrid genetic/greedy algorithm (extends Alg-class class).

Usage

Hybrid(pop_size = 20, nb_max_gen = 10, prob_mutation = 0.25, Kmax = 100)

Arguments

Value

a Hybrid-class object

Functions

• Hybrid: Hybrid algorithm class constructor

Slots

pop_size

size of the solutions populations (default to 20)

nb_max_gen

maximal number of generation to produce (default to 10)

prob_mutation

mutation probability (default to 0.25)

Kmax

maximum number of clusters (default to 100)

Examples

Hybrid()
Hybrid(pop_size = 100)

Generic method to extract the ICL value from an IclFit-class object

Description

This method take a IclFit-class object and return its ICL score.

Usage

ICL(fit)

## S4 method for signature 'IclFit'
ICL(fit)

Arguments

Value

The ICL value achieved

Methods (by class)

• IclFit: IclFit method

Description

An S4 abstract class to represent an icl fit of a clustering model.

Slots

K

a numeric vector of length 1 which correspond to the number of clusters

icl

a numeric vector of length 1 which store the the icl value

cl

a numeric vector of length N which store the clusters labels

obs_stats

a list to store the observed statistics of the model needed to compute ICL.

obs_stats_cst

a list to store the observed statistics of the model that do not depend on the clustering.

move_mat

binary matrix which store move constraints

train_hist

a data.frame to store training history (format depends on the used algorithm used).

name

generative model name

Description

An S4 class to represent a hierarchical path of solution.

Slots

path

a list of merge moves describing the hierarchy of merge followed to complete totally the merge path.

tree

a tree representation of the merges.

ggtree

a data.frame for easy plotting of the dendrogram

logalpha

a numeric value which corresponds to the starting value of log(alpha).

Description

List of edges of the network of Jazz musicians.

Usage

data(Jazz)

Format

An object of class sparseMatrix with the network adjacency matrix.

References

P.Gleiser and L. Danon , Community Structure in jazz, Adv. Complex Syst.6, 565 (2003) (Arxiv)

Examples

data(Jazz)

Generic method to get the number of clusters from an IclFit-class object

Description

This method take a IclFit-class object and return its ICL score.

Usage

K(fit)

## S4 method for signature 'IclFit'
K(fit)

Arguments

Value

The number of clusters

Methods (by class)

• IclFit: IclFit method

Description

An S4 class to represent a Latent Class Analysis model Such model can be used to cluster a data.frame $X$ with several columns of factors with the following generative model :

$\pi \sim \textrm{Dirichlet}(\alpha),$

$\forall k, \forall j, \quad \theta_{kj} \sim \textrm{Dirichlet}_{d_j}(\beta),$

$Z_i \sim \mathcal{M}_K(1,\pi),$

$\forall j=1, \ldots, p, \quad X_{ij}|Z_{ik}=1 \sim \mathcal{M}_{d_j}(1, \theta_{kj}),$

These classes mainly store the prior parameters value ($\alpha,\beta$) of this generative model. The Lca-class must be used when fitting a simple Latent Class Analysis whereas the LcaPrior-class must be used when fitting a CombinedModels-class.

Usage

LcaPrior(beta = 1)

Lca(alpha = 1, beta = 1)

Arguments

Value

a LcaPrior-class object

a Lca-class object

See Also

LcaFit-class, LcaPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Gmm, MoM, MoR, MultSbm, Sbm, greed()

Examples

LcaPrior()
LcaPrior(beta = 0.5)
Lca()
Lca(beta = 0.5)

Description

An S4 class to represent a fit of a Latent Class Analysis model for categorical data clustering, extend IclFit-class. The original data must be an n x p matrix where p is the number of variables and each variable is encoded as a factor (integer-valued).

Slots

model

a Lca-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• x_counts: matrix of size K*D with the number of occurrences of each modality for each clusters

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

coef,LcaFit-method

Description

An S4 class to represent a fit of a Latent Class Analysis model, extend IclPath-class.

Slots

model

a Lca-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• x_counts: matrix of size K*D with the number of occurrence of modality word in each clusters

path

a list of size K-1 with each part of the path described by:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• cl: vector of cluster indexes

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats a list with the following elements:

  • counts: numeric vector of size K with number of elements in each clusters

  • x_counts: matrix of size K*D with the number of occurrence of modality word in each clusters

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

plot,LcaFit,missing-method

Description

Compute the mutual information of two discrete samples

Usage

MI(cl1, cl2)

Arguments

Value

the mutual information between the two discrete samples

Examples

cl1 <- sample(2, 500, replace = TRUE)
cl2 <- sample(2, 500, replace = TRUE)
MI(cl1, cl2)

Description

An S4 class to represent a Mixture of Multinomial model. Such model can be used to cluster a data matrix $X$ with the following generative model :

$\pi \sim Dirichlet(\alpha)$

$Z_i \sim \mathcal{M}(1,\pi)$

$\theta_{k} \sim Dirichlet(\beta)$

$X_{i.}|Z_{ik}=1 \sim \mathcal{M}(L_i,\theta_{k})$

With $L_i=\sum_d=1^DX_{id}$. These classes mainly store the prior parameters value ($\alpha,\beta$) of this generative model. The MoM-class must be used when fitting a simple Mixture of Multinomials whereas the MoMPrior-class must be sued when fitting a CombinedModels-class.

Usage

MoMPrior(beta = 1)

MoM(alpha = 1, beta = 1)

Arguments

Value

a MoMPrior-class object

a MoM-class object

See Also

MoMFit-class, MoMPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoR, MultSbm, Sbm, greed()

Examples

MoMPrior()
MoMPrior(beta = 0.5)
MoM()
MoM(beta = 0.5)

Description

An S4 class to represent a fit of a degree corrected stochastic block model for co_clustering, extend IclFit-class.

Slots

model

a MoM-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• x_counts: matrix of size K*D with the number of occurrences of each modality for each clusters

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

coef,LcaFit-method

Description

An S4 class to represent a fit of a stochastic block model, extend IclPath-class.

Slots

model

a MoM-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• x_counts: matrix of size K*D with the number of occurrence of modality word in each clusters

path

a list of size K-1 with each part of the path described by:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• cl: vector of cluster indexes

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats a list with the following elements:

  • counts: numeric vector of size K with number of elements in each clusters

  • x_counts: matrix of size K*D with the number of occurrence of modality word in each clusters

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

plot,LcaFit,missing-method

Description

An S4 class to represent a multivariate mixture of regression model. The model follows [minka-linear](https://tminka.github.io/papers/minka-linear.pdf) . The model corresponds to the following generative model:

$\pi \sim Dirichlet(\alpha)$

$Z_i \sim \mathcal{M}(1,\pi)$

$V_k \sim \mathcal{W}(\varepsilon^{-1},n_0)$

$A_k \sim \mathcal{MN}(0,(V_k)^{-1},\tau XX^\top)$

$Y_{i.}|X_{i.}, A_k, Z_{ik}=1 \sim \mathcal{N}(A_k x_{i.},V_{k}^{-1})$

with $\mathcal{W}(\epsilon^{-1},n_0)$ the Wishart distribution and $\mathcal{MN}$ the matrix-normal distribution. The MoR-class must be used when fitting a simple Mixture of Regression whereas the MoRPrior-class must be used when fitting a CombinedModels-class.

Usage

MoRPrior(formula, tau = 0.001, N0 = NaN, epsilon = as.matrix(NaN))

MoR(formula, alpha = 1, tau = 0.1, N0 = NaN, epsilon = as.matrix(NaN))

Arguments

Value

a MoRPrior-class object

a MoR-class object

See Also

MoRFit-class, MoRPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MultSbm, Sbm, greed()

Examples

MoRPrior(y ~ x1 + x2)
MoRPrior(y ~ x1 + x2, N0 = 100)
MoRPrior(cbind(y1, y2) ~ x1 + x2, N0 = 100)
MoR(y ~ x1 + x2)
MoR(y ~ x1 + x2, N0 = 100)
MoR(cbind(y1, y2) ~ x1 + x2, N0 = 100)

Description

An S4 class to represent a fit of a multivariate mixture of regression model, extend IclFit-class.

Slots

model

a MoR-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• mvmregs: list of size $K$ with statistics for each clusters

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

coef,MoRFit-method

Description

An S4 class to represent a hierarchical fit of a multivariate mixture of regression model, extend IclPath-class.

Slots

model

a MoR-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• mvmregs: list of size $K$ with statistics for each clusters

path

a list of size K-1 with each part of the path described by:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats: a list with the following elements:

  • counts: numeric vector of size K with number of elements in each clusters

  • mvregs: list of size $K$ with statistics for each clusters

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

train_hist

data.frame with training history information (details depends on the training procedure)

Description

An S4 class to represent a greedy algorithm with multiple start (extends Alg-class class).

Usage

Multistarts(nb_start = 10)

Arguments

Value

a Multistarts-class object

Functions

• Multistarts: Multistarts algorithm class constructor

Slots

nb_start

number of random starts (default to 10)

Examples

Multistarts()
Multistarts(15)

Description

An S4 class to represent a Multinomial Stochastic Block Model. Such model can be used to cluster multi-layer graph vertex, and model a square adjacency cube $X$ of size NxNxM with the following generative model :

$\pi \sim Dirichlet(\alpha)$

$Z_i \sim \mathcal{M}(1,\pi)$

$\theta_{kl} \sim Dirichlet(\beta)$

$X_{ij.}|Z_{ik}Z_{jl}=1 \sim \mathcal{M}(L_{ij},\theta_{kl})$

With $L_{ij}=\sum_{m=1}^MX_{ijm}$. These classes mainly store the prior parameters value $\alpha,\beta$ of this generative model. The MultSbm-class must be used when fitting a simple MultSbm whereas the MultSbmPrior-class must be sued when fitting a CombinedModels-class.

Usage

MultSbmPrior(beta = 1, type = "guess")

MultSbm(alpha = 1, beta = 1, type = "guess")

Arguments

Value

a MultSbmPrior-class object

a MultSbm-class object

See Also

MultSbmFit-class, MultSbmPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MoR, Sbm, greed()

Examples

MultSbmPrior()
MultSbmPrior(type = "undirected")
MultSbm()
MultSbm(type = "undirected")

Description

An S4 class to represent a fit of a Multinomial Stochastic Block Model, extend IclFit-class.

Slots

model

a MultSbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• x_counts: cube of size KxKxM with the number of links between each pair of clusters

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

coef,MultSbmFit-method

Description

An S4 class to represent a hierarchical fit of a Multinomial Stochastic Block Model, extend IclPath-class.

Slots

model

a MultSbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• x_counts: matrix of size KxKxM with the number of links between each pair of clusters

path

a list of size K-1 with each part of the path described by:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• cl: vector of cluster indexes

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats: a list with the elements:

  • counts: numeric vector of size K with number of elements in each clusters

  • x_counts: matrix of size KxKxM with the number of links between each pair of clusters

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

plot,MultSbmFit,missing-method

Description

Categorical data from UCI Machine Learning Repository describing 8124 mushrooms with 22 phenotype variables. Each mushroom is classified as "edible" or "poisonous" and the goal is to recover the mushroom class from its phenotype.

Usage

data(mushroom)

Format

An R data.frame with a variable edibility used as label and 22 categorical variables with no names. More detail on the UCI webpage describing the data.

Source

https://archive.ics.uci.edu/ml/datasets/Mushroom

Examples

data(mushroom)

Description

Network of co-attendance occurrence attendance of suspected members of the Ndrangheta criminal organization at summits (meetings whose purpose is to make important decisions and/or affiliations, but also to solve internal problems and to establish roles and powers) taking place between 2007 and 2009.

Usage

data(Ndrangheta)

Format

An object of class list with two fields;

X

network adjacency matrix as a matrix of size 146x146

node_meta

data frame of nodes meta information with features :

Id

id of the node, rownames of network adjacency matrix

Locale

factor with the locali affiliation of the node , "OUT": Suspects not belonging to La Lombardia, "MISS": Information not available, other Locali Id.

Role

factor with the type of hierarchical position of the node "MISS": Information not available,"boss": high hierarchical position, "aff": affiliate

Source

ucinetsoftware/datasets/covert-networks

References

Extended Stochastic Block Models with Application to Criminal Networks, Sirio Legramanti and Tommaso Rigon and Daniele Durante and David B. Dunson, 2021, (arXiv:2007.08569).

Examples

data(Ndrangheta)

Description

NewGuinea a social network of 16 tribes, where two types of interactions were recorded, amounting to either friendship or enmity [read-cultures-1954].

Usage

data(NewGuinea)

Format

A binary array of size (16,16,3) the first layer encodes enmity, the second, the friendship relations. The third, no relations between the two tribes.

Source

https://networks.skewed.de/net/new_guinea_tribes

References

Kenneth E. Read, “Cultures of the Central Highlands, New Guinea”, Southwestern J. of Anthropology, 10(1):1-43 (1954). DOI: 10.1086/soutjanth.10.1.3629074

Examples

data(NewGuinea)

Description

Compute the normalized mutual information of two discrete samples

Usage

NMI(cl1, cl2)

Arguments

Value

the normalized mutual information between the two discrete samples

Examples

cl1 <- sample(2, 500, replace = TRUE)
cl2 <- sample(2, 500, replace = TRUE)
NMI(cl1, cl2)

Plot a DcLbmFit-class

Description

Plot a DcLbmFit-class

Usage

## S4 method for signature 'DcLbmFit,missing'
plot(x, type = "blocks")

Arguments

Value

a ggplot2 graphic

Plot a DcLbmPath-class

Description

Plot a DcLbmPath-class

Usage

## S4 method for signature 'DcLbmPath,missing'
plot(x, type = "tree")

Arguments

Value

a ggplot2 graphic

Plot a DcSbmFit-class object

Description

Plot a DcSbmFit-class object

Usage

## S4 method for signature 'DcSbmFit,missing'
plot(x, type = "blocks")

Arguments

Value

a ggplot2 graphic

See Also

plot,IclPath,missing-method

Plot a DiagGmmFit-class object

Description

Plot a DiagGmmFit-class object

Usage

## S4 method for signature 'DiagGmmFit,missing'
plot(x, type = "marginals")

Arguments

Value

a ggplot2 graphic

Plot a GmmFit-class object

Description

Plot a GmmFit-class object

Usage

## S4 method for signature 'GmmFit,missing'
plot(x, type = "marginals")

Arguments

Value

a ggplot2 graphic

Plot an IclPath-class object

Description

Plot an IclPath-class object

Usage

## S4 method for signature 'IclPath,missing'
plot(x, type = "tree")

Arguments

Value

a ggplot2 graphic

Plot a LcaFit-class object

Description

Plot a LcaFit-class object

Usage

## S4 method for signature 'LcaFit,missing'
plot(x, type = "marginals")

Arguments

Value

a ggplot2 graphic

Plot a MoMFit-class object

Description

Plot a MoMFit-class object

Usage

## S4 method for signature 'MoMFit,missing'
plot(x, type = "blocks")

Arguments

Value

a ggplot2 graphic

Plot a MultSbmFit-class object

Description

Plot a MultSbmFit-class object

Usage

## S4 method for signature 'MultSbmFit,missing'
plot(x, type = "blocks")

Arguments

Value

a ggplot2 graphic

Plot a SbmFit-class object

Description

Plot a SbmFit-class object

Usage

## S4 method for signature 'SbmFit,missing'
plot(x, type = "blocks")

Arguments

Value

a ggplot2 graphic

See Also

plot,IclPath,missing-method

Generic method to extract the prior used to fit IclFit-class object

Description

This method take a IclFit-class object and return the prior used.

Usage

prior(fit)

## S4 method for signature 'IclFit'
prior(fit)

Arguments

Value

An S4 object describing the prior parameters

Methods (by class)

• IclFit: IclFit method

Description

rdcsbm returns an adjacency matrix and the cluster labels generated randomly using a Degree Corrected Stochastic Block Model.

Usage

rdcsbm(N, pi, mu, betain, betaout)

Arguments

Details

It takes the sample size, cluster proportions and emission matrix, and as input and sample a graph accordingly together with the clusters labels.

Value

A list with fields:

• x: the count matrix as a dgCMatrix

• K: number of generated clusters

• N: number of vertex

• cl: vector of clusters labels

• pi: clusters proportions

• mu: connectivity matrix

• betain: normalized in-degree parameters

• betaout: normalized out-degree parameters

Description

rlbm returns the adjacency matrix and the cluster labels generated randomly with a Latent Block Model.

Usage

rlbm(Nr, Nc, pir, pic, mu)

Arguments

Details

This function takes the desired graph size, cluster proportions and connectivity matrix as input and sample a graph accordingly together with the clusters labels.

Value

A list with fields:

• x: the generated data matrix as a dgCMatrix

• clr: vector of row clusters labels

• clc: vector of column clusters labels

• Kr: number of generated row clusters

• Kc: number of generated column clusters

• Nr: number of rows

• Nc: number of column

• pir: row clusters proportions

• pic: column clusters proportions

• mu: connectivity matrix

Examples

simu <- rlbm(500, 1000, rep(1 / 5, 5), rep(1 / 10, 10), matrix(runif(50), 5, 10))

Description

rlca returns a data.frame with factor sampled from an lca model

Usage

rlca(N, pi, theta)

Arguments

Details

This function takes the desired graph size, cluster proportions and connectivity matrix as input and sample a graph accordingly together with the clusters labels.

Value

A list with fields:

• x: the multi-graph adjacency matrix as an array

• K: number of generated clusters

• N: number of vertex

• cl: vector of clusters labels

• pi: clusters proportions

• theta:

Examples

theta <- list(
  matrix(c(0.1, 0.9, 0.9, 0.1, 0.5, 0.5, 0.3, 0.7), ncol = 2, byrow = TRUE),
  matrix(c(0.5, 0.5, 0.3, 0.7, 0.05, 0.95, 0.3, 0.7), ncol = 2, byrow = TRUE),
  matrix(c(0.5, 0.5, 0.9, 0.1, 0.5, 0.5, 0.1, 0.9), ncol = 2, byrow = TRUE)
)
lca.data <- rlca(100, rep(1 / 4, 4), theta)

Description

rmm returns a count matrix and the cluster labels generated randomly with a Mixture of Multinomial model.

Usage

rmm(N, pi, mu, lambda)

Arguments

Details

It takes the sample size, cluster proportions and emission matrix, and as input and sample a graph accordingly together with the clusters labels.

Value

A list with fields:

• x: the count matrix as a dgCMatrix

• K: number of generated clusters

• N: number of vertex

• cl: vector of clusters labels

• pi: clusters proportions

• mu: connectivity matrix

• lambda: expectation of row sums

Description

rmreg returns an X matrix, a y vector and the cluster labels generated randomly with a Mixture of regression model.

Usage

rmreg(
  N,
  pi,
  A,
  sigma,
  X = cbind(rep(1, N), matrix(stats::rnorm(N * (ncol(A) - 1)), N, ncol(A) - 1))
)

Arguments

Details

It takes the sample size, cluster proportions and regression parameters matrix and variance as input accordingly

Value

A list with fields:

• X: the covariate matrix

• y: the target feature

• K: number of generated clusters

• N: sample size

• cl: vector of clusters labels

• pi: clusters proportions

• A: regression coefficients used in the simulation

• sigma: conditional variance

Description

rmultsbm returns the multi-graph adjacency matrix and the cluster labels generated randomly with a Multinomial Stochastic Block Model.

Usage

rmultsbm(N, pi, mu, lambda)

Arguments

Details

This function takes the desired graph size, cluster proportions and connectivity matrix as input and sample a graph accordingly together with the clusters labels.

Value

A list with fields:

• x: the multi-graph adjacency matrix as an array

• K: number of generated clusters

• N: number of vertex

• cl: vector of clusters labels

• pi: clusters proportions

• mu: connectivity matrix

• lambda:

Examples

simu <- rsbm(100, rep(1 / 5, 5), diag(rep(0.1, 5)) + 0.001)

Description

rsbm returns the adjacency matrix and the cluster labels generated randomly with a Stochastic Block Model.

Usage

rsbm(N, pi, mu)

Arguments

Details

This function takes the desired graph size, cluster proportions and connectivity matrix as input and sample a graph accordingly together with the clusters labels.

Value

A list with fields:

• x: the graph adjacency matrix as a dgCMatrix

• K: number of generated clusters

• N: number of vertex

• cl: vector of clusters labels

• pi: clusters proportions

• mu: connectivity matrix

Examples

simu <- rsbm(100, rep(1 / 5, 5), diag(rep(0.1, 5)) + 0.001)

Description

An S4 class to represent a Stochastic Block Model. Such model can be used to cluster graph vertex, and model a square adjacency matrix $X$ with the following generative model :

$\pi \sim Dirichlet(\alpha)$

$Z_i \sim \mathcal{M}(1,\pi)$

$\theta_{kl} \sim Beta(a_0,b_0)$

$X_{ij}|Z_{ik}Z_{jl}=1 \sim \mathcal{B}(\theta_{kl})$

These classes mainly store the prior parameters value $\alpha,a_0,b_0$ of this generative model. The Sbm-class must be used when fitting a simple Sbm whereas the SbmPrior-class must be used when fitting a CombinedModels-class.

Usage

SbmPrior(a0 = 1, b0 = 1, type = "guess")

Sbm(alpha = 1, a0 = 1, b0 = 1, type = "guess")

Arguments

Value

a SbmPrior-class object

a Sbm-class object

References

Nowicki, Krzysztof and Tom A B Snijders (2001). “Estimation and prediction for stochastic block structures”. In:Journal of the American statistical association 96.455, pp. 1077–1087

See Also

greed

SbmFit-class,SbmPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MoR, MultSbm, greed()

Examples

Sbm()
SbmPrior()
SbmPrior(type = "undirected")
Sbm()
Sbm(type = "undirected")

Description

An S4 class to represent a fit of a Stochastic Block Model, extend IclFit-class.

Slots

model

a Sbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over rows and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• x_counts: matrix of size K*K with the number of links between each pair of clusters

move_mat

binary matrix which store move constraints

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

coef,SbmFit-method

Description

An S4 class to represent a hierarchical fit of a stochastic block model, extend IclPath-class.

Slots

model

a Sbm-class object to store the model fitted

name

generative model name

icl

icl value of the fitted model

K

number of extracted clusters over row and columns

cl

a numeric vector with row and columns cluster indexes

obs_stats

a list with the following elements:

• counts: numeric vector of size K with number of elements in each clusters

• x_counts: matrix of size K*K with the number of links between each pair of clusters

path

a list of size K-1 with that store all the solutions along the path. Each element is a list with the following fields:

• icl1: icl value reach with this solution for alpha=1

• logalpha: log(alpha) value were this solution is better than its parent

• K: number of clusters

• cl: vector of cluster indexes

• k,l: index of the cluster that were merged at this step

• merge_mat: lower triangular matrix of delta icl values

• obs_stats: a list with the following elements:

  • counts: numeric vector of size K with number of elements in each clusters

  • x_counts: matrix of size K*K with the number of links between each pair of clusters

logalpha

value of log(alpha)

ggtree

data.frame with complete merge tree for easy plotting with ggplot2

tree

numeric vector with merge tree tree[i] contains the index of i father

train_hist

data.frame with training history information (details depends on the training procedure)

See Also

plot,SbmFit,missing-method

Description

An S4 class to represent a greedy algorithm with initialization from spectral clustering and or k-means (extends Alg-class class ).

Usage

Seed()

Value

a Seed-class object

Functions

• Seed: Seed algorithm class constructor

Examples

Seed()

Description

SevenGraders A small multiplex network of friendships among 29 seventh grade students in Victoria, Australia. Students nominated classmates for three different activities (who do you get on with in the class, who are your best friends, and who would you prefer to work with). Edge direction for each of these three types of edges indicates if node i nominated node j, and the edge weight gives the frequency of this nomination. Students 1-12 are boys and 13-29 are girls. The KONECT version of this network is the collapse of de Domenico's multiplex version.

Usage

data(SevenGraders)

Format

A binary array of size (29,29,3) containing directed graphs. The first layer encodes "getting along in class" while the second encodes the best-friendship (can be one-way). The third encodes the preferred work relation.

Source

https://networks.skewed.de/net/7th_graders

References

M. Vickers and S. Chan, "Representing Classroom Social Structure." Melbourne: Victoria Institute of Secondary Education, (1981).

Examples

data(SevenGraders)

Description

Print an IclPath-class object, model type and number of found clusters are provided.

Usage

## S4 method for signature 'IclFit'
show(object)

Arguments

Value

None (invisible NULL). No return value, called for side effects.

Description

performs regularized spectral clustering of a sparse adjacency matrix

Usage

spectral(X, K)

Arguments

Value

cl Vector of cluster labels

References

Tai Qin, Karl Rohe. Regularized Spectral Clustering under the Degree-Corrected Stochastic Block Model. Nips 2013.

Description

Convert a binary adjacency matrix with missing value to a cube

Usage

to_multinomial(X)

Arguments

Value

a cube

Description

Young people survey data from Miroslav Sabo and available on the Kaggle platform. This is an authentic example of questionnaire data where Slovakian young people (15-30 years old) were asked musical preferences according to different genres (rock, hip-hop, classical, etc.).

Usage

data(Youngpeoplesurvey)

Format

An R data.frame with columns containing each of the 150 original variables of the study.

Source

https://www.kaggle.com/miroslavsabo/young-people-survey

Examples

data(Youngpeoplesurvey)